Abstract: A Zeeman magnetic field can induce a Fulde-Ferrell-Larkin-Ovchinnikov FFLOphase in spin-singlet superconductors. Here we argue that there is anon-trivial solution for the FFLO vortex phase that exists near the uppercritical field in which the wavefunction has only spatial line nodes that formintricate and unusual three-dimensional structures. These structures include acrisscrossing lattice of two sets of non-parallel line nodes. We show thatthese solutions arise from the decay of conventional Abrikosov vortices intopairs of fractional vortices. We propose that neutron scattering studies canobserve these fractional vortex pairs through the observation of a lattice of1-2 flux quanta vortices. We also consider related phases innon-centrosymmetric NC superconductors.